It's the future. Mars has been successfully colonized. Since the completion of the carbon nanotube space elevator 100 years ago, Mars' route capacity greatly increased and new settlements flourished. The United States of Mars is now a prosperous independent planet. Terraforming will still take centuries to transform Mars into a fully habitable planet and human colonies will be confined for a while to domes providing air, water, food and protection from cosmic rays.

Venus' atmosphere has also been colonized, floating aerostat glide in the Venusian atmosphere at 50 km altitude where the temperature is around 280K, circling the planet every 96 earth hours. These aerostats are filled with breathable air similar to that found on earth. Breathable air is a lifting gas on Venus (like helium on Earth) and it can lift entire research lab colonies. The upper atmosphere of Venus protects the settlements from cosmic rays.
Those colonies are mostly used for scientific missions because large-scale floating settlements are impractical. Terraforming Venus will take even longer than terraforming Mars, getting rid of the crushing 93 bar atmosphere and decreasing the 750 K temperature will require technologies and energy levels that we haven't mastered yet.

Asteroids in the Asteroid Belt have been colonized mostly for mining. Some of these asteroids have rare metals but apart from automated mining factories, there's not much interest in settling on those tiny objects.

The United States of Earth is looking for new challenges to foster humanity and wants to colonize planets beyond the asteroid belt.

After decades of probing, scientists' consensus is that a layer of liquid water exists deep beneath the icy surface of Titan, Callisto, Ganymede, Europa, Ceres and Enceladus. That heat from tidal flexing and the inner core allows the subsurface ocean to remain liquid.

The liquid ocean on these icy moons is estimated to be at least 10 km below the frozen ice surface. Surface temperature is a chilling 100K, the atmosphere is almost non-existent, gravity is very low, cosmic ray radiation is quite high. These rocks are much harder to colonize than Venus or Mars but that won't stop us right? The question is how would we establish colonies on these planets?

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$\begingroup$Wikipedia has some nice pages about colonizing planets and moons... did you even try googling?$\endgroup$
– L.Dutch♦Nov 29 '17 at 6:47

$\begingroup$I wonder why Mars ends up being the United States of Mars? Did the history repeat itself? Poor Martians, I guess...$\endgroup$
– OlgaNov 29 '17 at 12:19

$\begingroup$In case you haven't read it the tooltip for the downvote button says "This question does not show any research effort; it is unclear, or not useful."$\endgroup$
– sphenningsNov 29 '17 at 15:40

$\begingroup$Thanks for all the links, I googled a bit and searched wikipedia but didn't find any good answer.$\endgroup$
– FredNov 30 '17 at 0:55

1 Answer
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So you already have several colonies in several resource points, so if space trade is feasible due to the asteroids and space elevators, the new Jupiter moon colony could be entirely space-manufactured.
If the government is content with the plan, then designs, target locations, and orbital mechanics could be planned easily using a probe from a Mars space elevator.

Now you've got resources, a planned orbit, and the designs. Now the question is Why.

Why do you need to build on Jupiter's moons? What use would they bring.

One simple word: water

Not for drinking, but for rocket fuel.

Europa could contain literally tonnes of hydrogen for rocket fuel, which could be dedicated to extreme projects like a deep-space cruise, interstellar transit, or for tourism.

Plus, if He-3 fusion engines are developed, then Jupiter could be used for a fusion fuel depot, increasing the value of a Jupiter moon station.

While this answer doesn't give technical feedback, it does give reasons and motives to build a lunar base near Jupiter.